DOI:
10.1039/D0QI00981D
(Research Article)
Inorg. Chem. Front., 2021,
8, 156-163
Anomalous dielectric behaviour during the monoclinic to tetragonal phase transition in La(Nb0.9V0.1)O4†
Received
13th August 2020
, Accepted 23rd October 2020
First published on 27th October 2020
Abstract
La(Nb0.9V0.1)O4 has been shown by in situ Raman spectroscopy and X-ray diffraction to undergo a ferroelastic phase transition from monoclinic fergusonite to tetragonal scheelite (TM–T) at 350 °C, accompanied by 3.55% spontaneous strain and an abrupt change in the thermal expansion coefficient (αL) from +15.5 ppm °C−1 to +11.4 ppm °C−1. Assuming a linear relationship between polarizability and temperature, an anomalous decrease in relative permittivity (εr) at TM–T is predicted from the Clausius–Mosotti relation and Shannon's additive rule. Such an anomalous decrease in εr in a phase transition has not previously been observed in ferroic and linear dielectrics and may aid in the design of novel microwave dielectric composites.
Introduction
Microwave (MW) dielectric ceramic materials are widely used as dielectric resonators, filters, antenna substrates, and capacitors for wireless and mobile communication, and radar and satellite positioning systems.1–4 The large εr (real part of permittivity) of MW dielectric ceramic materials helps in reducing the dimensions of MW devices and the low dielectric loss (high quality factor, Q) enhances the frequency selectivity.2–5 Furthermore, their temperature stability with respect to resonant frequency (TCF) ensures that related devices work from −45 to 85 °C. 5th generation wireless systems (5G) have gradually come on-line in recent years and offer ultra-wideband, ultra-high speed, and ultra-low latency.6–8 The frequency spectrum of 5G is generally divided into millimeter wave, mid-band and low-band. The millimeter wave (above 24 GHz) is yet to be exploited but materials with εr < 10 are likely to be utilised.7–10 Low-band refers to available frequency ranges at <1 GHz, whereas mid-band exploits the 2–6 GHz interval and is the most widely deployed. To attain the required data transmission rates, massive MIMO (multiple input and multiple output) and Multi-User MIMO (MU-MIMO) antennas are employed that are composed of large numbers of interconnected devices.11–15 Massive MIMO functions through mini base stations and exploits materials with εr = 20, such as MgTiO3–CaTiO3, (Ca1+xSm1−x)(Al1−xTix)O4, and Li2TiO3 due to their high Q and low TCF.7,16–19
Alongside the three materials mentioned above, fergusonite-structured LnNbO4 (Ln = La, Sm, Nd etc.) ceramics have attracted attention due to their high Q and εr ∼ 20.20–23 Kim et al. first reported the microwave dielectric properties of LaNbO4 ceramic sintered at 1250 °C with εr = 19.3, a high Qf (Q × resonant frequency, f) ∼ 54
400 GHz and TCF = +9 ppm °C−1.20 Substitutions of La or Nb by isovalent ions plus the use of sintering aid in further improving the microwave dielectric properties.21–23 In our previous work,21 we demonstrated that 10 mol% substitution of V5+ for Nb5+ increases the TCF from +9 ppm °C−1 to +110 ppm °C−1.
TCF is approximately half the temperature coefficient εr (τε) according to:
| ![image file: d0qi00981d-t1.tif](/image/article/2021/QI/d0qi00981d/d0qi00981d-t1.gif) | (1) |
where
αl is the linear thermal expansion coefficient (below +15 ppm °C
−1 for ceramics). Hence, any abrupt change in TCF is normally attributed to a change in
τε usually caused by a structural phase transition. Phase transitions which show an increase in
εr are commonplace in ferroic materials as commonly observed for paraelectric to ferroelectric/antiferroelectric, ferroelectric to ferroelectric, octahedral tilt and paraelastic to ferroelastic transformations.
24–31
All the above phase transitions occur through classical softening of a transverse optical mode, consistent with the Lyddane–Sach–Teller relation.32 Since the maximum value of εr occurs at the phase transition temperature (PTT/TC), τε is largely positive below, but negative above the PTT, provided εr is not too high. This principle is the basis for the well-established relationship between the tolerance factor and τε described by Reaney et al.33 in which octahedral tilting induces an increase in εr at the PTT in Sr- and Ba-based complex perovskites. The TCF follows the inverse trend. Similarly BiVO4 undergoes a second-order ferroelastic phase transition from the monoclinic (I2/a) to tetragonal scheelite (I41/a) structure at 255 °C, at which temperature a maximum value of εr is observed.31,34–38 Furthermore in (Li0.5xBi1−0.5x)(MoxV1−x)O4 (0 ≤ x ≤ 0.25) ceramics, peaks in εr are observed at the PTT38,39 with the corresponding changes in TCF.
LaNbO4 also undergoes a ferroelastic phase transition from a monoclinic fergusonite to tetragonal scheelite structure at ∼480 °C.40–45 From previous studies,21,46 V5+ substitutes for Nb5+ on the B site and lowers the PTT to room temperature, where the tetragonal scheelite structure is stabilized for x = 0.225. However, in La(Nb,V)O4 solid solutions, the TCF decreases from a large positive (+100 ppm °C−1) to a large negative value (−40 ppm °C−1), the opposite trend to that which is typically observed at PTTs. This anomalous behaviour may be further elucidated by undertaking a detailed study of the crystal structure as a function of temperature. In the present work, therefore, we present in situ XRD and Raman data in combination with thermal expansion measurement which are interpreted through Landau theory, Shannon's additive rule, and the Clausius–Mosotti relation. Understanding this behavior might lead to design of temperature stable composite materials in the future.
Materials and methods
Material synthesis
Preparation of the La(Nb0.9V0.1)O4 ceramic was described in detail in our previous work.21
Material characterization
Room temperature XRD patterns were acquired using a Bruker D2 Phaser in the 2θ range of 10–70°, with a step size of 0.02. In situ XRD patterns were collected using a Siemens D5000 diffractometer from 30–500 °C using Pt foil as the holder for high temperature measurements. Results were analyzed by the Rietveld profile refinement method, using the FULLPROF program. In situ Raman spectra were obtained with a Renishaw Raman microscope (model InVia) using a 532 nm solid state (100 mW) laser and a Linkam stage (model THMS600). Dielectric properties measurements were performed on sintered ceramics, diameter ∼ 10 mm and thickness ∼ 1 mm, coated with gold using an LCR (Agilent E4980A) and homemade heating system from 25 to 680 °C at 10 kHz, 100 kHz, 250 kHz and 1 MHz with a heating rate of 1 °C min−1.
Results and discussion
In situ XRD patterns of the La(Nb0.9V0.1)O4 ceramic in the temperature range 30–500 °C and cell parameters as a function of temperature are shown in Fig. 1(a) and (b). At room temperature, La(Nb0.9V0.1)O4 crystallized with a monoclinic fergusonite structure (I2/c), with V5+ ions substituting for Nb5+. As the temperature increased, some characteristic peaks such as (121) and (130), (002) and (200) converged and merged into a single peak at ∼350 °C, indicating a continuous structural transition from a monoclinic fergusonite structure to a tetragonal scheelite structure (I41/a). The cell parameter a decreased with temperature while c increased and became equal to a at 350 °C, commensurate with a linear decrease in β from 93° to 90°, Fig. 1(b). All data are therefore consistent with the premise that ∼10 mol% V5+ substitutes for Nb5+, decreasing the distortion of the BO4 tetrahedra, and lowering the ferroelastic phase transition temperature from 480 °C to 350 °C for undoped LaNbO4 and La(Nb0.9V0.1)O4, respectively.
![image file: d0qi00981d-f1.tif](/image/article/2021/QI/d0qi00981d/d0qi00981d-f1.gif) |
| Fig. 1 (a) In situ XRD patterns of the La(Nb0.9V0.1)O4 ceramic from 30–500 °C. (b) Cell parameters as a function of temperature. (c) Cell volume and thermal expansion vs. temperature. (d) Schematic of the change in the crystal structure projected along the b axis. (e and f) Experimental (circles) and calculated (line) XRD profiles for La(Nb0.9V0.1)O4 at room temperature (Rp = 8.34%, Rwp = 11.5%, and Rexp = 6.52%) and 400 °C (Rp = 10.9%, Rwp = 14.9%, and Rexp = 9.84%). (The short vertical lines below the patterns mark Bragg reflections. The bottom continuous line is the difference between the observed and the calculated intensity.) | |
Fig. 1(c) shows the cell volume and thermal expansion data of La(Nb0.9V0.1)O4 as a function of temperature. As the temperature increased from 25 °C to 300 °C, the cell volume increased linearly from 331.19 Å3 to 336.19 Å3 corresponding to a gradient of +56 ppm °C−1. The cell volume further increased to 337.53 Å3 at 500 °C, but the gradient decreased to +20 ppm °C−1, suggesting a structural phase transition at ∼350 °C. Thermal expansion coefficients also followed the same trend (Fig. 1(c)), abruptly changing from +15.5 ppm °C−1 to +11.4 ppm °C−1 at the proposed PTT. Fig. 1(d) is a schematic illustrating the change in the crystal structure along the b axis. In the fergusonite structure, B site ions (Nb,V) are located in the center of distorted tetrahedra with two B–O bond lengths, resulting in different values of a and c, and a β angle >90 degrees. Above 350 °C, the B–O bond lengths in the tetrahedra become equal and the tetrahedral distortion disappears, coincident with β approaching 90 degrees. Cell refinements of fergusonite- and scheelite-structured La(Nb0.9V0.1)O4 at room temperature and 400 °C are shown in Fig. 1(e) and (f), respectively. The refined lattice parameters of La(Nb0.9V0.1)O4 at room temperature are a = 5.23654(7) Å, b = 11.6033(4) Å, c = 5.50762(4) Å, and β = 92.894 (4) ° with the space group I2/c (15) using data (ICSD # 81616) from Machida et al.47 The refined lattice parameters of scheelite La(Nb0.9V0.1)O4 at 400 °C are a = c = 5.3781(5) Å, b = 11.6783(7) Å with a space group I41/a (88) from (ICSD # 37139) reported by David.48 The atomic fractional coordinates and structural details are listed in Tables 1 and 2. Clear domains could be observed from the room temperature TEM images of the La(Nb0.9V0.1)O4 ceramic as shown in Fig. S1 in the ESI† and agree well with the XRD data.
Table 1 Refined atomic fractional coordinates from XRD data for the La(Nb0.9V0.1)O4 sample at room temperature and the lattice parameters are a = 5.23654(7) Å, b = 11.6033(4) Å, c = 5.50762(4) Å, β = 92.894 (4) °. The space group is I2/c (15)
Atom |
Site |
Occ. |
x
|
y
|
z
|
La |
4e |
0.5 |
0.25000 |
0.13539 |
0.00000 |
Nb |
4e |
0.45 |
0.25000 |
0.61890 |
0.00000 |
V |
4e |
0.05 |
0.25000 |
0.61890 |
0.00000 |
O1 |
8f |
1.00 |
0.04142 |
0.71988 |
0.28695 |
O2 |
8f |
1.00 |
1.02836 |
0.44614 |
0.19333 |
Table 2 Refined atomic fractional coordinates from the XRD data for the La(Nb0.9V0.1)O4 sample at 400 °C and the lattice parameters are a = c = 5.3781(5) Å, b = 11.6783(7) Å. The space group is I41/a (88)
Atom |
Site |
Occ. |
x
|
y
|
z
|
La |
4b |
0.25 |
0.00000 |
0.25000 |
0.62500 |
Nb |
4a |
0.20 |
0.00000 |
0.25000 |
0.12500 |
V |
4a |
0.05 |
0.00000 |
0.25000 |
0.12500 |
O |
16f |
1.000 |
0.15639 |
0.02148 |
0.20595 |
The ferroelastic phase transition from monoclinic fergusonite to tetragonal scheelite is associated with an increase in point group symmetry from 2/m to 4/m and results in merging of two crystal orientation states (S1 and S2) above the PTT. Hence, second-rank strain tensors can be employed to describe these two orientation states caused by the relative ‘monoclinic’ displacements to the paraelastic scheelite phase:49,50
| ![image file: d0qi00981d-t2.tif](/image/article/2021/QI/d0qi00981d/d0qi00981d-t2.gif) | (2) |
where R and R
T are the 90° rotation matrix and its transposition, respectively. As reported by Schlenker
et al.,
51 strain tensor components can be calculated from the cell parameters:
where
am,
bm,
cm and
βm are the cell parameters of the monoclinic phase, and
ct and
cb are the extrapolated tetragonal phase cell parameters. As described by Aizu,
49 ferroelasticity can be quantified using the spontaneous strain tensors and the two possible orientation states of La(Nb
0.9V
0.1)O
4 are presented as follows:
| ![image file: d0qi00981d-t7.tif](/image/article/2021/QI/d0qi00981d/d0qi00981d-t7.gif) | (4) |
| ![image file: d0qi00981d-t8.tif](/image/article/2021/QI/d0qi00981d/d0qi00981d-t8.gif) | (5) |
where
![image file: d0qi00981d-t9.tif](/image/article/2021/QI/d0qi00981d/d0qi00981d-t9.gif)
is the longitudinal strain and
ν =
e12 is the shear strain. It follows that the magnitude of the spontaneous strain is:
| ![image file: d0qi00981d-t10.tif](/image/article/2021/QI/d0qi00981d/d0qi00981d-t10.gif) | (6) |
The spontaneous strain of the La(Nb0.9V0.1)O4 ceramic is ∼3.55% at room temperature, approximately half of that of undoped LaNbO4 ceramic (6.79%).
According to Landau's theory,52 the order parameter η (eqn (7)) may be used to describe the deviation from the paraelastic phase:
| ![image file: d0qi00981d-t11.tif](/image/article/2021/QI/d0qi00981d/d0qi00981d-t11.gif) | (7) |
where
Tc is the PTT, (350 °C) and
T is temperature. The magnitude of the spontaneous strain of La(Nb
0.9V
0.1)O
4 is proportional to
η according to:
where
k is a constant (0.03725). The
η ×
k and
es values as a function of temperature are plotted in
Fig. 2. From room to the phase transition temperature, the agreement between
η ×
k and
es is obtained, confirming that the transition is of second order.
![image file: d0qi00981d-f2.tif](/image/article/2021/QI/d0qi00981d/d0qi00981d-f2.gif) |
| Fig. 2 Magnitude of the spontaneous strain and order parameter η of the La(Nb0.9V0.1)O4 ceramic as a function of temperature. | |
Group theory predicts that there are 18 Raman active modes for a monoclinic fergusonite structure (I2/a) and the irreducible representation of the modes is:53,54
| Γ = 8Ag + 10Bg + 8Au + 10Bu, | (9) |
where
Ag and
Bg are Raman active while
Au and
Bu are IR active. For the tetragonal scheelite structure (
I4
1/
a), the irreducible representation according to the group theory is given by:
55,56 | Γ = 3Ag + 5Bg + 5Eg + 5Au + 3Bu + 5Eu, | (10) |
where all the
Ag,
Bg and
Eg are Raman active and all the
Au and
Eu are IR active. The correlation of the representations is at
Γ points of the
I2/
a and
I4
1/
a space groups. The phase transition in La(Nb
0.9V
0.1)O
4 may be described as a proper ferroelastic with strain as the primary order parameter, dominated by a soft acoustic phonon (marked
Q in
Fig. 3a). Based on Landau's theory,
54ωQ below the PTT (
TC) is given as follows:
| ![image file: d0qi00981d-t12.tif](/image/article/2021/QI/d0qi00981d/d0qi00981d-t12.gif) | (11) |
where
ωQ0 is the frequency at
TC,
δc′
0 is a spontaneous shear strain parameter, and
T0 is the temperature at which the ferroelastic phase becomes unstable.
ωQ decreases linearly with temperature in the ferroelastic phase but remains constant in the paraelastic phase, which agrees with the experimental results,
Fig. 3b, where
ωQ0 is ∼90 cm
−1. For BiVO
4, the ferroelastic → paraelastic phase transition is driven by a temperature-dependent
Bg optic mode coupled to the acoustic soft mode as described by Pinczuk
et al.37,57 In contrast to BiVO
4, no soft optical mode has been observed from room temperature to 500 °C, which defines the phase transition in LaNbO
4 to be purely ferroelastic with strain as the sole order parameter.
54,58 Hence, the Lyddane–Sachs–Teller (LST) relation is not followed.
![image file: d0qi00981d-f3.tif](/image/article/2021/QI/d0qi00981d/d0qi00981d-f3.gif) |
| Fig. 3 (a) Raman shifts of La(Nb0.9V0.1)O4 from 25–500 °C and (b) selected modes as a function of temperature. | |
ε
r and dielectric loss of the La(Nb0.9V0.1)O4 ceramic as a function of temperature at different frequencies (10 kHz, 100 kHz, 250 kHz, 1 MHz and 8.5 GHz) are shown in Fig. 4. Different from BiVO4 ferroelastic ceramics and other ferroics as shown in Fig. 5b, an anomalous εr minimum value was observed at 10 kHz, 100 kHz, 250 kHz, and 1 MHz. Due to the limitation in microwave dielectric measurement, we did not obtain the wide temperature microwave εr spectrum but the present data show an apparent decrease of permittivity vs. temperature, which gives a large positive TCF value. Compared with εr, there is no abnormality observed from dielectric loss as shown Fig. 4(b). In the microwave region, polarizability is the sum of both ionic and electronic components. Shannon59 suggested that the molecular polarizability (α) of complex substances may be estimated by summing α of the constituent ions which for La(Nb0.9V0.1)O4 is:
| αLa(Nb0.9V0.1)O4 = αLa3+ + 0.9 × αNb5+ + 0.1 × αV5+ + 4αO2− = 17.98 Å3, | (12) |
where the ionic polarizabilities of La
3+, Nb
5+, V
5+ and O
2− are 6.07 Å
3, 3.97 Å
3, 2.92 Å
3 and 2.01 Å
3, respectively.
59 Considering the Clausius–Mosotti (C–M) relation,
60 | ![image file: d0qi00981d-t13.tif](/image/article/2021/QI/d0qi00981d/d0qi00981d-t13.gif) | (13) |
where
V is the cell volume (331.19/4 = 82.8 Å
3). The calculated
εr is 31.1, much larger than the measured value (∼20) at room temperature. As reported by Tsunekawa
et al.,
40,44,53 BO
4 tetrahedra are distorted in the fergusonite structure. The distorted tetrahedra have reduced B–O bond lengths, dampened B–O lattice vibrations and thereby decreased polarizability. Furthermore, macroscopic polarizability also includes additional terms related to the crystal structure and local anisotropy. As reported by Feteira
et al.,
61 polarizabilities of lanthanides (Ln) were derived from the rare-earth aluminates system and it became evident that Ln (
e.g. La
3+ = 4.68 Å
3) has lower values than reported by Shannon.
59
![image file: d0qi00981d-f4.tif](/image/article/2021/QI/d0qi00981d/d0qi00981d-f4.gif) |
| Fig. 4 (a and b) εr and dielectric loss of the La(Nb0.9V0.1)O4 ceramic as a function of temperature at different frequencies (10 kHz, 100 kHz, 250 kHz, 1 MHz and 8.5 GHz). | |
![image file: d0qi00981d-f5.tif](/image/article/2021/QI/d0qi00981d/d0qi00981d-f5.gif) |
| Fig. 5 (a) Calculated dielectric constant of the La(Nb0.9V0.1)O4 ceramic on assumptions of fixed and linear increasing polarizabilities and (b) schematic of εr of typical electro-ceramics vs. temperature. | |
The C–M relationship indicates that the εr of a specific compound is determined both by the cell volume and molecular polarizability. For La(Nb0.9V0.1)O4, as the temperature increased, the cell volume increased linearly below and above 350 °C but with different gradients. Based on the assumption that the molecular polarizability does not change with temperature, εr, calculated using eqn (13), is plotted in Fig. 5a which reveals a linear decrease below and above 350 °C but at different gradients. There is therefore an anomaly at 350 °C but not a minimum value of εr. However, if we assume that the molecular polarizability increases with temperature and follows a simple linear relation
| αLa(Nb0.9V0.1)O4 = α0 + (T − TR) × k, | (14) |
where
α0 is the room temperature molecular polarizability, 17.975 Å
3,
TR is room temperature and
k (0.00075) is a temperature-dependent constant; the combined effect of the cell volume and molecular polarizability
vs. T gives a minimum value of
εr at the PTT as shown in
Fig. 5a. Although this is a rough calculation, it gives a clear explanation for the dielectric minimum of the La(Nb
0.9V
0.1)O
4 ceramic at the PTT, at which point a decrease in thermal expansion coefficient occurs. In
Fig. 5b, we summarize the possible curves of
εrvs. T for a ferroelectric, relaxor, antiferroelectric, ferroelastic, paraelectric and linear dielectric material. The purely ferroelastic character and the sudden decrease in thermal expansion coefficient for La(Nb
0.9V
0.1)O
4 are anomalous compared with conventional ferroics and dielectrics.
Conclusions
The La(Nb0.9V0.1)O4 ceramic was determined by in situ XRD analysis to undergo a ferroelastic phase transition from a monoclinic fergusonite structure to a tetragonal scheelite structure at ∼350 °C. Raman analysis identified strain as the sole order parameter with a value of 3.55% at room temperature, almost half of that of the pure LaNbO4 ceramic. At the PTT, there was an abrupt change of the thermal expansion coefficient from +15.5 ppm °C−1 to +11.4 ppm °C−1, related to the anomalous change in the cell volume. Assuming a linear increase in polarizability, the minimum value of εr at the PTT for La(Nb0.9V0.1)O4 was predicted from the Clausius–Mosotti relation and Shannon's additive rule. Compared with ferroelectrics, relaxors, antiferroelectrics, ferroelastics, paraelectrics and linear dielectrics, the behaviour of εr in La(Nb0.9V0.1)O4vs. temperature is anomalous and may have novel applications in temperature stable composite ceramics.
Conflicts of interest
There are no conflicts to declare.
Acknowledgements
This work was supported by the National Key Research and Development Program of China (Grant 2017YFB0406301), the Sustainability and Substitution of Functional Materials and Devices EPSRC (EP/L017s563/1), the National Natural Science Foundation of China (51972260, 52072295), the State Key Laboratory of Electrical Insulation and Power Equipment (Grant EIPE19210), the Fundamental Research Funds for the Central University, and the 111 Project of China (B14040).
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Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0qi00981d |
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